MANAMA, Bahrain — The United States has tripled the number of airstrikes this year against Al Qaeda’s branch in Yemen, one of the deadliest and most sophisticated terrorist organizations in the world. American allies have pushed the militants from their lucrative coastal strongholds. And the Pentagon recently boasted of killing key Qaeda leaders and disrupting the group’s operations.

Yet the top United States counterterrorism official and other American intelligence analysts concede the campaign has barely dented the terrorist group’s ability to strike United States interests.

“It doesn’t feel yet that we’re ahead of the problem in Yemen,” Nicholas J. Rasmussen, who stepped down this month after three years as the director of the National Counterterrorism Center, said in an interview. “It continues to be one of the most frustrating theaters in our counterterrorism work right now.”

Even as President Trump lauds the demise of the Islamic State’s self-proclaimed caliphate in Iraq and Syria, the threat of a terrorist attack — with the most commonly feared target a commercial airliner — emanating from the chaotic, ungoverned spaces of Yemen remains high on the government’s list of terrorism concerns. The group formally known as Al Qaeda in the Arabian Peninsula, or A.Q.A.P., has dogged Mr. Trump since his first days in office, when the president authorized an ill-fated raid on a Qaeda hide-out that left one member of the Navy’s elite SEAL Team 6 dead.

The fight against Al Qaeda is a different military campaign in a different part of Yemen than the one helping fuel the humanitarian disaster gripping the country, most visibly in the west. Yemen, one of the poorest nations in the Arab world, has been convulsed by civil strife since the Houthis, Shia rebels from the north aligned with Iran, stormed the capital, Sana, in 2014 and then ousted the government of President Abdu Rabbu Mansour Hadi, the Americans’ main counterterrorism partner.

In March 2015, Saudi Arabia and a coalition of Arab nations began a military campaign aimed at pushing back the Houthis and restoring the government. That campaign has so far failed to do so and has instead caused the world’s most severe humanitarian crisis, the worst outbreak of cholera in contemporary history and widespread child malnutrition.

Al Qaeda exploited the security vacuum and in 2015 took control of large parts of land in the south, including Al Mukalla, Yemen’s fifth-largest city and a major source of port revenue.

The Qaeda wing in Yemen remains so nefarious in part because the group has spent years inventing explosives that are difficult to detect, including trying to disguise bombs in devices like cellphones. It has tried at least three times to blow up American airliners, without success. And its most notorious bomb maker, Ibrahim Hassan al-Asiri, remains at large and is training protégés, intelligence officials say.

“Still the world’s most dangerous man,” David H. Petraeus, the former C.I.A. director and a retired four-star general, said of Mr. Asiri at a security conference here this month.

With no real functioning government in Yemen, the United States does not have the Special Operations forces or C.I.A. presence on the ground that it had before Yemen’s civil war, American counterterrorism officials say, and thus lacks the deeper understanding of the situation there that would give officials confidence about Al Qaeda’s plotting.

“We can’t distinguish between people who are still pretty serious threats and guys who are just working with them because they need help,” said Gerald M. Feierstein, a former United States ambassador to Yemen.

Over the past 18 months, however, American-backed Yemeni and Emirati troops have increased a shadow war in the country’s central and southern regions against more than 3,000 members of the Qaeda affiliate and its tribal confederates, driving them into the rugged, mountainous interior.

Since Feb. 28, as part of President Trump’s intensified campaign against terrorists, the United States has conducted nearly 130 airstrikes in Yemen — mostly against Qaeda militants with about 10 against Islamic State fighters, according to the Pentagon’s Central Command. That is up from 38 strikes in 2016.

The Central Command boasted in an unusual statement this month that the airstrikes and Special Operations raids had killed several important Qaeda leaders.

The attacks “have put pressure on A.Q.A.P.’s network, severely limiting their freedom of movement, disrupting the organization’s ability to recruit and train, and limiting A.Q.A.P.’s ability to plan and execute external operations,” Lt. Col. Earl Brown, a Central Command spokesman, said in an email soon after the command issued an assessment of the campaign on Dec. 20.

In the south, more than 4,000 Yemeni troops backed by United Arab Emirates forces recently announced the death or capture of several Qaeda militants in Abyan and Shabwa provinces. Yemeni government security forces have been deployed in most of former Qaeda strongholds but the militants still exist in Baydha and Shabwa’s Sayed district.

The Yemenis have also captured some important Qaeda operatives. Their interrogations have given the Yemeni forces and their American and Emirati partners valuable insights into the insurgents’ leadership hierarchy, propaganda plans and local networks, a United States official said.

“We have disrupted A.Q.A.P., but I remain concerned,” Gen. Joseph L. Votel, the head of the Central Command, said in an interview during the Manama Dialogue security conference here. “This is an organization that’s proved resilient over time. This is an extraordinarily dangerous element of Al Qaeda.”

Lora Shiao, the acting director of intelligence for the National Counterterrorism Center, told a Senate hearing this month that the Qaeda branch “continues to exploit the conflict in Yemen to gain new recruits and secure areas of safe haven, contributing to its enduring threat.”

Al Qaeda is not the only terrorist group seeking to take advantage of the turmoil in Yemen. An affiliate of the Islamic State there has doubled in size in the past year, according to the Central Command. When asked at the same Senate hearing this month which failed state offered the best location for a terrorist group, Mark E. Mitchell, a senior Pentagon official overseeing Special Operations policy, told lawmakers, “First of all would be Yemen.”

Yemen specialists say it is not at all clear that the escalating use of military force in the country is tied to any wider counterterrorism approach that draws on diplomacy, humanitarian and stabilization efforts, and cooperation on intelligence sharing and law enforcement that can make for sustainable gains against Al Qaeda.

“I’m worried that this is a military effort, however effective it may be, divorced from a broader strategic approach,” said Joshua A. Geltzer, who was senior director for counterterrorism at the National Security Council during the Obama administration.

Mr. Rasmussen explained that while the military campaign had put pressure on the Qaeda network in Yemen, the lack of a government to work with had hampered efforts. “I still feel we’re lacking a lot of that right now,” Mr. Rasmussen said. “We’ve lost a lot of insight into what happens on the ground in Yemen.”

Just five days after taking office, Mr. Trump approved sending in the Navy’s SEAL Team 6, hoping the raid against a Qaeda compound would scoop up cellphones and laptop computers that could yield valuable clues about one of the world’s most dangerous terrorist groups.

The death of a commando, Chief Petty Officer William Owens, came after a chain of mishaps and misjudgments that plunged the team into a ferocious 50-minute firefight that also left three others wounded and a $75 million aircraft deliberately destroyed. Several civilians were also killed.

American-backed Emirati troops reclaimed Al Mukalla in April 2016, but in recent weeks, military checkpoints have sprouted throughout the city. The security measures intensified in response to the concerns of government officials that Qaeda militants might infiltrate the large number of families who have fled a Houthi crackdown in Sana on supporters of former President Ali Abdullah Saleh, who was killed by the Houthis this month after breaking an alliance with them.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: U.S. Pounds Al Qaeda in Yemen, But Barely Dents Risk of Attack. Order Reprints | Today’s Paper | Subscribe